A sequence of numbers is called a wiggle sequence if the differences between successive numbers strictly alternate between positive and negative. The first difference (if one exists) may be either positive or negative. A sequence with fewer than two elements is trivially a wiggle sequence.

For example, `[1,7,4,9,2,5]` is a wiggle sequence because the differences `(6,-3,5,-7,3)` are alternately positive and negative. In contrast, `[1,4,7,2,5]` and `[1,7,4,5,5]` are not wiggle sequences, the first because its first two differences are positive and the second because its last difference is zero.

Given a sequence of integers, return the length of the longest subsequence that is a wiggle sequence. A subsequence is obtained by deleting some number of elements (eventually, also zero) from the original sequence, leaving the remaining elements in their original order.

Example 1:

``````Input: [1,7,4,9,2,5]
Output: 6
Explanation: The entire sequence is a wiggle sequence.
``````

Example 2:

``````Input: [1,17,5,10,13,15,10,5,16,8]
Output: 7
Explanation: There are several subsequences that achieve this length. One is [1,17,10,13,10,16,8].
``````

Example 3:

``````Input: [1,2,3,4,5,6,7,8,9]
Output: 2
``````

Follow up: Can you do it in O(n) time?

• 上升序列。在这种情况下，上升序列必定可以使下降序列的长度增加一，当然这里理解起来有点复杂，需要分各种情况讨论：
• 该子序列的值都比下降序列最后一个元素的值小。这种情况的话，其实还是能使得下降序列的长度增加一的，让下降序列的前一个元素指向子序列的第一个元素就可以。
• 该子序列的值都比下降序列最后一个元素的值大，很好理解，直接下降序列长度加一。
• 下降序列，和上升序列一样。

``````class Solution {
public:
int wiggleMaxLength(vector<int>& nums) {
if (nums.size() == 0) {
return 0;
}
int up = 1;
int down = 1;

for (int i = 1; i < nums.size(); i++) {
if (nums[i] > nums[i - 1]) {
// Increase down length
if (down + 1 > up) {
up = down + 1;
}
} else if (nums[i] < nums[i - 1]) {
// Increase up length
if (up + 1 > down) {
down = up + 1;
}
}
}
return max(down, up);
}
};
`````` ### 作者 